In our analysis, focusing on for asymptotically flat, stationary BPS solutions with bi-axisymmetry and reflection symmetry in the five-dimensional ungauged minimal supergravity, we regard motion of particles as a two-dimensional potential problem.
As discussed for several BPS black holes in the same theory [1]}, [2]}, [3]}, [4]}, [5]}, one can replace a problem of whether there exist stable bound orbits for particles with a simple problem of whether the two-dimensional effective potential has a negative local minimum.
First, we numerically show the existence of stable bound orbits for massive particles for the microstate geometries with three Gibbons-Hawking centers.
Next, we numerically show that there can be stable bound orbits of massive and massless particles for the microstate geometries with five Gibbons-Hawking centers which has the same mass and angular momenta as the BMPV black holes.
Moreover, we also study the five center solutions whose angular momenta are larger than the BMPV black holes.
